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Since it is his/her thirteen birthday, that would me 13-8=5 years back. We know a year is 12 months so 12*5=60 We have to go 60 months back. So the first step would be to go back in time as much as possible, just before 60 months or just after 60 months. 60/7=8 with a remainder of 4. 8*5= 40 steps, but we went 25 steps backwards as stated so that wouldn't make sense. Starting over, I use the maximum amount of steps we can go backwards, which is using pedometer B 5 times. That would bring us back 35 months, only a bit more than half.
60-35=25 months to go, we can accomplish more by using Pedometer C, 8 times which will bring us back 24 months. So now 25-24=1. One more month to go and we went 16 steps forward. But we used the pedometer 13 times, so let's start again.
I start again using Pedometer B, 5 times, so we need to go back 25 months. This time, I used Pedometer A 4 times, going back in time 16 months and going 28 steps forward. I used the Pedometers 9 times now, 3 uses left, and with those three uses left, I use Pedometer C, 3 times. 9 months back adding up to the 25 we need to go to the 8th birthday. Also going 6 steps forward.
Grade 7 POTW: From 13 to 8 is 5 years, since 13-8= 5. The question has three pedometers that go back in time in months only, so I would convert years to months, which is 5*12 = 60 months. Using the three pedometers, I would have to get to 60 months.
The question also states that you go 25 steps backward and use the three pedometers a total of 12 times. The only way to go 25 steps is using Pedometer B, since it is the only one that goes backward. 25/5 = 5 5*7=35 months. 60-35 = 25 months left. I would then have to use Pedometer A 4 times, which is going back 16 months back, and Pedometer C 3 times, which is 9 months back. This adds up to 25 months, the exact amount I need.
Double checking, 4+5+3 = 12 pedometer uses in total, so the answer is correct. I used Pedometer A 4 times, and each time I take 7 steps forward, so that is 4*7 = 28 steps forward. Pedometer C was used 3 times, and each time I take 3 steps forward, so 3*3 = 9.
Instead of 3*3 in pedometer C, it is actually 3*2. This gives me 6 steps forward. Adding 6 to 28, this would be a total of 34 steps forward. Therefore, the total number of steps forward is 34. -Alan---
Grade 8 POTW: For this question, there are two unknown values, the money he has saved, and what the question has asked, how many songs he downloaded.
Right now I am going to focus on the reason why there is a difference between the different stores.
For the first store, he needs 17 dollars. For the second store, he has 5 dollars extra. The only difference between these two stores is that one costs 80 cents per download, and one costs a dollar. Since the amount of song downloads are equal, I do not have to consider that as a factor. 1-0.8 = 0.2. This is the difference of the two store amounts per download, which is 20 cents. I would have to find the difference between the two amounts. 17-(-5) = 22 dollars. The reason of why the amount is negative 5 is because he does not need 5 dollars, he has 5 dollars left. 22/0.2 = 110. This means that he downloaded 110 songs.
Double check: 110*0.8 = 88 dollars. This is the amount he would have to pay at the second store. With 5 dollars left, he would save 88+5 = 93 dollars. 110*1 = 110 dollars. This is the amount he would have to pay at the third store. 110-93 = 17 dollars. This is one of the conditions: He needs 17 dollars more than he already has, which is 93 dollars.
This proves that 110 is correct, therefore the number of songs Salim wants to download is 110 songs. -Alan-
You use pedometer A 4 times, pedometer B 5 times, and pedometer C 3 times. I got this by first finding out how much I'd have to go back. 13-8=5 so I'd have to go back 5 years. Since the pedometers use months to time travel I converted 5 years to months. 5*12=60 so I'd have to travel back 60 months. Then since I have to take 25 steps back I know how much times I have to use pedometer B because that's the only pedometer that takes steps back. For each use you'd take 5 steps back so 25/5=5. That means you'd have to use pedometer B 5 times. Since each use goes back 7 months that means we traveled back 35 months(7*5) in 5 uses. 60-35=25 so we have to travel back 25 months in 7 uses of pedometers A and C. Then I used guess and check to solve. If we use pedometer A 7 times you go back 28 months. This is too much and knowing how if I replace a use of pedometer A with C I will reduce the amount traveled by 1 month. So then i use pedometer A 4 times and C 3 times. This is 12 uses (4+5+3=12) and 60 months(16+35+9=60). Then for the amount of steps forward A uses 7 steps per and C uses 2 steps per. (7*4)+(3*2)=34 so I took 34 steps forward.
Since you are travelling to your 8th birthday, or 5 years back in time, you are travelling for 60 months. Because you took 25 backwards steps, that means that you used Pedometer B 5 (25/5) times, meaning that you went back 35 months in time. However, you still have 25 months to go. Because you have 7 pedometer uses left, using guess and check, I figured out that you use Pedometer A 4 times (go back 16 months), and Pedometer C 3 times (go back 9 months). Because pedometer A and C are the only pedometers in which you can take forward steps, since you used pedometer a 4 times (7x4=28), and Pedometer C 3 times (2x3=6), you took 24 steps forward.
Since it is his/her thirteen birthday, that would me 13-8=5 years back. We know a year is 12 months so 12*5=60
ReplyDeleteWe have to go 60 months back. So the first step would be to go back in time as much as possible, just before 60 months or just after 60 months.
60/7=8 with a remainder of 4. 8*5= 40 steps, but we went 25 steps backwards as stated so that wouldn't make sense.
Starting over, I use the maximum amount of steps we can go backwards, which is using pedometer B 5 times. That would bring us back 35 months, only a bit more than half.
60-35=25 months to go, we can accomplish more by using Pedometer C, 8 times which will bring us back 24 months. So now 25-24=1. One more month to go and we went 16 steps forward. But we used the pedometer 13 times, so let's start again.
I start again using Pedometer B, 5 times, so we need to go back 25 months. This time, I used Pedometer A 4 times, going back in time 16 months and going 28 steps forward. I used the Pedometers 9 times now, 3 uses left, and with those three uses left, I use Pedometer C, 3 times. 9 months back adding up to the 25 we need to go to the 8th birthday. Also going 6 steps forward.
So
Pedometer A: Uses: 4 Steps Forward: 28
Pedometer B: Uses: 5 Steps Backward: 25
Pedometer C: Uses: 3 Steps Forward: 9
28+9= 37 steps forward.
Doesn't pedometer C use 2 steps?
DeleteYeah, it does
DeleteGrade 7 POTW:
ReplyDeleteFrom 13 to 8 is 5 years, since 13-8= 5. The question has three pedometers that go back in time in months only, so I would convert years to months, which is 5*12 = 60 months. Using the three pedometers, I would have to get to 60 months.
The question also states that you go 25 steps backward and use the three pedometers a total of 12 times. The only way to go 25 steps is using Pedometer B, since it is the only one that goes backward.
25/5 = 5
5*7=35 months.
60-35 = 25 months left.
I would then have to use Pedometer A 4 times, which is going back 16 months back, and Pedometer C 3 times, which is 9 months back. This adds up to 25 months, the exact amount I need.
Double checking, 4+5+3 = 12 pedometer uses in total, so the answer is correct.
I used Pedometer A 4 times, and each time I take 7 steps forward, so that is 4*7 = 28 steps forward.
Pedometer C was used 3 times, and each time I take 3 steps forward, so 3*3 = 9.
28+9 = 37 steps forward in total.
-Alan
Instead of 3*3 in pedometer C, it is actually 3*2.
DeleteThis gives me 6 steps forward.
Adding 6 to 28, this would be a total of 34 steps forward.
Therefore, the total number of steps forward is 34.
-Alan---
Grade 8 POTW:
ReplyDeleteFor this question, there are two unknown values, the money he has saved, and what the question has asked, how many songs he downloaded.
Right now I am going to focus on the reason why there is a difference between the different stores.
For the first store, he needs 17 dollars. For the second store, he has 5 dollars extra. The only difference between these two stores is that one costs 80 cents per download, and one costs a dollar. Since the amount of song downloads are equal, I do not have to consider that as a factor.
1-0.8 = 0.2. This is the difference of the two store amounts per download, which is 20 cents.
I would have to find the difference between the two amounts.
17-(-5) = 22 dollars. The reason of why the amount is negative 5 is because he does not need 5 dollars, he has 5 dollars left.
22/0.2 = 110. This means that he downloaded 110 songs.
Double check:
110*0.8 = 88 dollars. This is the amount he would have to pay at the second store.
With 5 dollars left, he would save 88+5 = 93 dollars.
110*1 = 110 dollars. This is the amount he would have to pay at the third store.
110-93 = 17 dollars. This is one of the conditions: He needs 17 dollars more than he already has, which is 93 dollars.
This proves that 110 is correct, therefore the number of songs Salim wants to download is 110 songs.
-Alan-
Maxwell and Avi Grade 7 POTW:
ReplyDeleteThey took 34 steps forward while using the pedometers. We did our work on a whiteboard.
You use pedometer A 4 times, pedometer B 5 times, and pedometer C 3 times. I got this by first finding out how much I'd have to go back. 13-8=5 so I'd have to go back 5 years. Since the pedometers use months to time travel I converted 5 years to months. 5*12=60 so I'd have to travel back 60 months. Then since I have to take 25 steps back I know how much times I have to use pedometer B because that's the only pedometer that takes steps back. For each use you'd take 5 steps back so 25/5=5. That means you'd have to use pedometer B 5 times. Since each use goes back 7 months that means we traveled back 35 months(7*5) in 5 uses. 60-35=25 so we have to travel back 25 months in 7 uses of pedometers A and C. Then I used guess and check to solve. If we use pedometer A 7 times you go back 28 months. This is too much and knowing how if I replace a use of pedometer A with C I will reduce the amount traveled by 1 month. So then i use pedometer A 4 times and C 3 times. This is 12 uses (4+5+3=12) and 60 months(16+35+9=60). Then for the amount of steps forward A uses 7 steps per and C uses 2 steps per. (7*4)+(3*2)=34 so I took 34 steps forward.
ReplyDeleteGrade 7 POTW
ReplyDeleteSince you are travelling to your 8th birthday, or 5 years back in time, you are travelling for 60 months. Because you took 25 backwards steps, that means that you used Pedometer B 5 (25/5) times, meaning that you went back 35 months in time. However, you still have 25 months to go. Because you have 7 pedometer uses left, using guess and check, I figured out that you use Pedometer A 4 times (go back 16 months), and Pedometer C 3 times (go back 9 months). Because pedometer A and C are the only pedometers in which you can take forward steps, since you used pedometer a 4 times (7x4=28), and Pedometer C 3 times (2x3=6), you took 24 steps forward.